Entanglement generation and distribution is an important problem in
performing quantum-information tasks, such as quantum computation
and quantum teleportation [1]}, [2]}, [3]}. Many
results showed that entanglement existed naturally in the spin chain
when the temperature is at zero. Due to its potential applications,
the pairwise entanglement of anisotropic Heisenberg model was
extensively studied recently [4]}. A typical example is the
exactly solved one-dimensional infinite-lattice anisotropic \(XY\) 
model using the Jordan-Wigner transform to obtain the pairwise
entanglement [5]}, [6]}, [7]}, [8]}. By using the
Bethe ansatz solution, the entanglement in infinite isotropic
Heisenberg rings was calculated [9]}. In recent years, the
study of the dynamics of entanglement has attracted much attention
due to the manipulation of quantum systems. The dynamics of
entanglement in different systems were investigated [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}. The
effects of anisotropy interaction on the evolution of entanglement
were investigated [18]}, such a global quench could actually
be realized for atoms in optical lattices [21]}. Moreover,
the effects of a bond defect on the entanglement dynamics in a local
quench were studied [22]} and the evolution of
one-dimensional quantum lattice systems was investigated when the
ground state was perturbed by altering one site in the middle of the
chain [23]}, [24]}, [25]}, [26]}, [27]}, [28]}.
Recently, Bose exploited a global quench dynamics in spin chains for
distant pairwise entanglement, which could be used for quantum
communication [29]}. It would be interesting to investigate
the overall pairwise entanglement dynamics between the nearest two
qubits in the spin chain when several typical quenches are performed
in the system.
